The filtering problem concerns the recursive estimation of a partially observed Markov process conditioned on a path of observations. It is found
in a wide class of real applications, including finance, applied mathematics and engineering; see [1]} for instance. This article focusses upon the computation of
the normalizing constant for certain classes of filtering problems, to be introduced below. These normalizing constants can be of interest in statistics and engineering
for model selection and/or parameter estimation.
